Or she's just human like the rest of us and didn't immediately associate "aircraft on this message I received" with "aircraft I'm now handling" until she had said it aloud. I've certainly done that before and I'd imagine when your main focus is on safely working several aircraft at once, information from outside your normal, everyday work flow is probably not going to get the same mental treatment as information coming from the inbound aircraft that just contacted you or the flight strip you were just handed.
Or maybe someone just told her as she was issuing the clearance to the aircraft. So rather than saying standby, she just said everything in one sentence without hesitation.
And I doubt a print out was given to her to interupt her. Towers aren't as high tech as we would like them to be.